Question: f(x) = \frac{x - 4}{x^2 - 64}

Solution

To determine the horizontal asymptotes for the function \[ f(x) = \frac{x - 4}{x^2 - 64} \] we compare the degrees of the numerator and the denominator. The degree of the numerator is 1 (since it’s \(x - 4\)). The degree of the denominator is 2 (since it’s \(x^2 - 64\)). Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at \(y = 0\). Thus, there is one horizontal asymptote at \(y = 0\). Select “One” for the number of horizontal asymptotes and plot a line at \(y = 0\) on the graph.